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Graph algebras establish a connection between directed graphs without multiple edges and special universal algebras of type (2, 0). We say that a graph G satisfies an identity s ≈ t if the corresponding graph algebra A(G) satisfies s ≈ t. A graph G = (V, E) is called an (xy)x ≈ x(yy) graph if the graph algebra A(G) satisfies the equation (xy)x ≈ x(yy). An identity s ≈ t of terms s and t of any type τ is called a hyperidentity of an algebra A if whenever the operation symbols occurring in s and t are replaced by any term operations of A of the appropriate arity, the resulting identities hold in A. In this paper we characterize (xy)x ≈ x(yy) graph algebras, identities and hyperidentities in (xy)x ≈ x(yy) graph algebras.

HYPERIDENTITIES IN (xy)x ≈x(yy) GRAPH ALGEBRAS OF TYPE (2,0)